I feel like people are somewhat exaggerating how complicated dual type moves would be. It would take some getting used to for sure but I doubt people would be scratching their heads over it.
The difficulty in understanding it could depend on one thing though:
1. If you have a Water/Electric move, are the types independent of each other? (i.e is it super effective against Fire, Rock, Ground and Flying?)
2. Or do the types combine into one pseudo type? (i.e is it super effective against Fire, Rock, Flying but has no effect on Ground?)
If it's the first one I figure it's a lot simpler to understand, you're just appending the effectiveness of two types together rather than the latter which is adding them together.